Method of and an Apparatus for Determining Information Relating to a Projectile, Such as a Golf Ball

ABSTRACT

An apparatus and a method of providing information relating to a projectile, such as a sports ball, such as a golf ball. The apparatus and method provide better estimations of e.g. the landing point of the projectile or its position in general in that an oscillating signal caused e.g. by multiple path reflections of the radiation, is identified and may be removed in order to generate the “true” signal used for the landing point determination. This oscillating signal may be used for quantifying an error of the landing point determination or may be used for providing information relating to the surroundings of the projectile during its flight.

The present invention relates to a method and an apparatus fordetermining information relating to a projectile, such as a rifleprojectile, a missile or, a sports ball, such as a golf ball, or anotherobject adapted to be launched. The information relates to the projectileat least partly while the projectile is in flight. In a number ofembodiments, the information sought may be the actual path taken by theprojectile, the deviation thereby from a predetermined path, the landingpoint, or the like.

A number of apparatus and methods are known for determining informationfrom flying projectiles. Such apparatus may comprise the providing oftransmitting equipment inside the projectile or e.g. a bat used forhitting a sports ball. Other equipment uses a radar for receivingradiation from the projectile, such as from a golf ball, and fordetermining information from the projectile. However, such apparatus isnot able to determine the actual landing point of the ball in that,normally, the radar is turned off, lacks sensitivity, or the measurementstopped before the ball lands.

Golf radars are described in: WO03/032006, WO 91/06348, U.S. Pat. Nos.5,700,204, 6,547,671, 5,092,602, 4,509,052, 3,798,644, 6,133,946,5,489,099, 6,244,971, 6,456,232, and 5,495,249 as well as inJP-A-6126015 and 8266701.

A problem encountered using radar or the like on a flying projectile isthat of the radiation transmitted from the projectile to the receivermay take multiple paths. Such multiple paths will have different pathlengths, whereby the signals from the individual paths will interferewith each other. This interference will influence rather drastically onthe final result, such as a determination of a velocity or position ofthe projectile.

Especially the determination of a landing point of the projectile isdifficult in that the radiation from the projectile will experience alsothe ground especially when close to the ground, where the detection iscritical. At this point, the interference of the signals will be large,whereby the signal will vary and actually reaches zero even though theprojectile is still in flight. In this respect, it should be noted thatthe signal needs not actually reach zero, but it will be smaller than adetection threshold, whereby it will “formally” be zero in the sensethat it is not detectable within the detection limit.

This multi-path problem may be solved by preventing radiation from allbut one such path from reaching the detector. This, however, may bedifficult to obtain especially when the projectile is close to theground and is far away from the detector.

This problem is seen both in golf, cricket and baseball, where balls arehit large distances and where, such as for training purposes orentertainment purposes, it is desired to know where the ball landed orother characteristics of the ball flight path.

One aspect of the invention relates to another manner of handling themulti-path situation. This aspect relates to a method of determininginformation relating to a projectile, the method comprising:

-   -   receiving electromagnetic radiation emitted from or reflected by        the projectile at least partly while it is in flight, and        providing a corresponding signal,    -   generating an altered signal by removing, from the provided        signal, an oscillating signal, and    -   determining the information relating to the projectile from the        altered signal.

In the present context, normally, the radiation emitted/reflected fromthe projectile takes more than one path toward the receiver, whereby theradiation received has the same frequency/wavelength or is within apredetermined wavelength interval. In this manner, wavelength filteringmay be provided in order to filter away noise caused by radiationoutside this frequency or this interval.

The oscillating signal may be caused (at least partly) by the radiationtaking more than one path, where the radiation from the multiple pathsinterfere and cause the oscillating signal.

Also, that the radiation is received at least partly while theprojectile is in flight relates to the fact that radiation received andinformation derived from the projectile before flying or after havinglanded may be very valuable in combination with the radiation received(and information derived) during the flight.

This oscillation is caused by the projectile moving, whereby the pathlengths in the different paths vary and cause, together with thewavelength of the radiation, an oscillation of the resulting signalreceived.

The oscillating signal is continuous and may, but need not, besinusoidal. In fact, the oscillation would, if caused by this multi-patheffect, increase in amplitude over time and it will also change infrequency. The amplitude will depend on the reflection of thesurroundings, normally the ground. The oscillation will depend on theshape of the surroundings (path length difference) as well as theprojectile trajectory and relative position of the receiver. For a golfball trajectory, the frequency of the oscillating signal is, for areceiver placed a couple of meters behind the launch point, normally inthe interval of 0.5-10 Hz. For riffle projectiles, missiles or artilleryprojectiles the frequency of the oscillating signal is slightly lower,normally in the interval of 0.1-2 Hz.

Naturally, any type of radiation may be used, such as visible light, IR,NIR, UV, Microwaves or radio waves may be used. Also sound, such asultrasound may be used.

The corresponding signal may be a signal representing signal strength, afrequency, a wavelength, intensity, a phase or any other characteristicof the radiation received. Normally, the corresponding signal representsthis characteristic over a period of time.

The information derived relating to the projectile may be the positionthereof, the velocity, spin, rotation, height, acceleration, path, orthe like.

In the present context, the removal of the oscillating signal from thecorresponding signal may be a coherent adding of the unwanted signalshifted 180 degrees in phase or any other manner of taking away theoscillating signal from the other signal.

The resulting, altered signal will be a smooth signal, representing theactual position and movement of the projectile.

In one embodiment, the generating step comprises performing an averagingoperation comprising averaging the provided signal over a predeterminedtime period. Averaging over a period of time larger than a full periodor variation (of a non-periodical signal) of the oscillating signal willaverage out the oscillating signal and provide an altered signal withcomponents having a frequency lower than a signal having a period of theaveraging time period. This is one manner of removing the oscillatingsignal.

Another manner is one wherein the generating step comprises tracking theoscillating signal and subtracting the oscillating signal from theprovided signal. This tracking may be obtained on the basis of aknowledge of the frequency (or frequency interval) of the oscillatingsignal. In this manner, the signal may be identified and tracked,whereby subtraction is easy.

As mentioned above, the provided signal may, due to interference, reachzero even though the actual signal desired—the altered signal—has notreached zero. Thus, one embodiment relates to a method where thegenerating step comprises generating the altered signal for apredetermined period of time after, that the provided signal reacheszero. If the provided signal subsequently rises above zero, theproviding of the altered signal may continue, until the provided signalhas not increased over zero for the predetermined point in time. In thismanner, any interference will not untimely stop the determination.

As mentioned above, the oscillating signal may be caused by interferencefrom multiple paths. Thus, the receiving step may comprise receiving theradiation from at least two different directions or paths.

In one embodiment, the determining step comprises determining aparameter of the projectile at a first point in time and estimating,from the determined parameter, the parameter at a second, later, pointin time. One manner of performing this estimation is to perform it usinga predetermined relation between the parameter and time. In thatsituation, the parameter will have a predetermined course or developmentover time. One such parameter is a distance between a means receivingthe radiation and the projectile. When monitoring the parameter, such asthe distance, at a first point in time or during a first period of time,it is possible to predict the parameter/distance at a later point intime.

When the corresponding signal provided is a signal representing anintensity of the radiation received, the determining step may comprisedetermining a distance between a means receiving the radiation and theprojectile. This is due to the fact that the intensity emitted orreflected by the projectile may be independent of an orientation of theprojectile or it is a priori known, whereby the intensity/signalstrength received will relate to the distance between the projectile andthe receiver. Naturally, if a radiation/sound emitter is used, thedistance between the projectile and the emitter should also be takeninto account.

A particularly interesting embodiment is one which is able to determinethe landing point or landing spot of the projectile. Hitherto, landingpoint determination has been performed on the basis of knowledge of onlypart of the path or the projectile during flight. This, however, haspresented uncertainties in the determination. One reason for the priorart techniques not putting emphasis on the signals from a projectileclose to the ground may be the above-mentioned oscillating multiple-pathsignals.

In this embodiment, the generating step comprises generating the alteredsignal, until the altered signal fulfils a predetermined criterion, thedetermining step further comprising providing, as the information, anestimate of a landing point of the projectile.

Thus, now that it is possible to actually remove the oscillating signal,which in multiple-path situations is the strongest, when the projectileis close to the ground, it is possible to keep providing a reliablealtered signal. Then, the certain criterion is preferably related to asituation where it is probable that the projectile has, in fact, landed.

In this situation, the landing point of the projectile will normally bethe spot of impact between the projectile and the ground. In thesituation where the projectile subsequently bounces back up and againhits the ground, the landing point is the first point of impact.

The predetermined criterion will relate to what the provided and actualsignals represent. When these signals represent a signal strength oramplitude, the predetermined criteria may be an absolute or a relativesignal strength/intensity/amplitude, a predetermined absolute orrelative drop/increase of the strength/intensity/amplitude, apredetermined course or development over time.

One particular manner is to have the determining step compriseperforming a filtering using a time constant larger than a period of theoscillating signal, and to determine a landing point as a point wherethe signal level has decreased a predetermined amount, such as 3 dB.

The frequency or period of the oscillating signal depends on both thetrajectory of the projectile as well as the height thereof above theground (or the distance to the reflecting surface) and the velocity ofthe projectile. Thus, a golf ball may give rise to a period in theinterval of 0.5-10 Hz, whereas a projectile launched by a rifle or ahandgun may give rise to longer periods, such as 0.1-2 Hz, againdepending on the actual trajectory.

One manner of using this landing point is one where the determining stepcomprises providing as the information an estimate of a distance betweenthe landing point of the projectile and a predetermined target. This maybe useful for practising hitting a target, such as a flag on a golfcourse, where it may then be desirable to also know the distance, andoften also the direction and height difference, from the target to thereceiver. Thus, using this set-up, it is possible to determine theactual distance between the target and the landing point without havingto travel to the target area.

Another manner of using the landing point information is to have thedetermining step comprise providing as the information an estimate of adeviation from a predetermined direction and a determined direction ofthe projectile. This determined direction may e.g. be determined fromthe landing point.

This deviation may be an angular deviation between the two directions,but the deviation may also be determined as a 3 dimensional distancebetween the intended and the actual directions at the distance of thelanding point of the projectile.

In order to determine the actual path/direction of the projectile, it isdesired that the determining step further comprises determining a launchposition of the projectile, the determined direction of the projectilebeing a direction between the launch position and the landing point. Anumber of manners exist of determining the launch position of theprojectile. One method is to simply dictate this position in relation tothe receiver.

The launch position may be a position where the projectile leaves theground plane, as would be the case for a golf ball, it might be aposition from where the projectile leaves a launch pad, such as a rifle,or it may be a position where the projectile is impacted in order toinitiate its path, such as where it is hit by a hand, a bat, or thelike.

A second aspect relates to e.g. the use of the provided signal eventhough the oscillating signal forms part thereof. This aspect relates toa method of determining information relating to a projectile, the methodcomprising:

-   -   receiving electromagnetic radiation emitted from or reflected by        the projectile at least partly while it is in flight, and        providing a corresponding signal,    -   identifying whether an amplitude of the provided signal varies        more than a predetermined threshold,    -   determining the information from the corresponding signal, and    -   quantifying an uncertainty of the determination of the        information from the variation of the amplitude.

Thus, the oscillating signal is accepted, and an uncertainty of theinformation is quantified on the basis of thestrength/intensity/amplitude of the oscillating signal. Thisquantification is a standard technique in statistical analysis.

Naturally, the oscillating signal could also be removed by the methodfurther having a step of generating the altered signal by removing fromthe provided signal an oscillating signal, the method further comprisingthe step of determining further information from the altered signal. Theinformation determined from the altered signal may be that described inrelation to the first aspect. Thus, his generating step could compriseperforming an averaging operation comprising averaging the providedsignal over a time period larger than a predetermined time period ortracking the oscillating signal and subtracting the oscillating signalfrom the provided signal.

As mentioned above, the generating step could generate the alteredsignal for a predetermined period of time after, that the providedsignal reaches zero, in order to more precisely determine e.g. a landingpoint.

The oscillating signal may be caused by multiple-path problems causedwhen the receiving step comprises receiving the radiation from at leasttwo different directions or paths.

Also, the determining step could comprise determining a parameter of theprojectile at a first point in time and estimating, from the determinedparameter, the parameter at a second, later, point in time. Thisestimation may be performed using a predetermined relation between theparameter and time, and the parameter determined may be a distancebetween a means receiving the radiation and the projectile.

The corresponding signal provided may be a signal representing anintensity of the radiation received. Then, the determining step couldcomprise determining a distance between a means receiving the radiationand the projectile.

A third aspect of the invention relates to the use of the oscillatingsignal for providing information. This aspect relates to a method ofdetermining information relating to the surroundings of a projectile,the method comprising:

-   -   receiving electromagnetic radiation emitted from or reflected by        the projectile at least partly while it is in flight, and        providing a corresponding signal,    -   generating an altered signal by isolating, from the provided        signal, an oscillating signal, and    -   determining, as the information and from the altered signal, In        one situation, an angle to vertical of, and/or a distance to, a        surface over which the projectile flies and/or a reflection        coefficient of the radiation of a surface over which the        projectile flies.

When the oscillating signal relates to a multiple-path situation, itshould be remembered that one path may be that directly between theprojectile and the receiver, but that the others must have experiencedat least one reflection from or by the surroundings. This reflectionprovides information about the reflecting coefficient and the angle of,and/or a distance to, the point of reflection. During flight of theprojectile, this point will also move in the surroundings.

This may be combined with knowledge, such as provided using the first orsecond aspects, of the position of the projectile.

A fourth aspect relates to a method of determining a distance between aprojectile and a radiation receiver, the method comprising the steps of:

-   -   receiving electromagnetic radiation emitted from or reflected by        the projectile at least partly while it is in flight,    -   determining an intensity of the radiation received and a        distance between the receiver and the projectile at a first        point in time,    -   determining, at a second, later point in time, a second        intensity of the radiation received, and    -   determining from a mathematical relation between the first and        second intensities determined, a distance, at the second point        in time, between the receiver and the projectile.

This is especially interesting, if it may be assumed that the emissionor reflection from the projectile toward the receiver is constant, inthat the difference between the intensities may then simply only relateto the difference in distance. In that situation, the mathematicalrelation is simple.

A situation which may complicate the matter slightly is that where thereceiver(s), or any transmitter providing the radiation, have an angledependent emission or sensitivity/gain, in which the angle or positionof the projectile also has to be taken into account. This, however, is aknown procedure e.g. in radar technology.

Naturally, if a transmitter is used for providing the radiation/soundtoward the projectile, the distance between the transmitter and theprojectile also has to be taken into account.

The first point in time may be a point in time before, at, or afterlaunch of the projectile where the position of the projectile is known.

The present distance determination may be used for determining theactual distance to the projectile or it may be used for checking anotherdistance measurement.

In any of the above aspects, the step of providing the correspondingsignal could comprise providing a signal representing an intensity orpower of the received radiation within a predeterminedfrequency/wavelength interval. In that manner, a filtering of unrelatedradiation/sound may be performed.

Also, the method according to any of the above aspects may furthercomprise the initial step of providing electromagnetic radiation towardthe projectile while in flight. In that manner, the wavelength/frequencyof the radiation/sound as well as the intensity/signal strength thereofmay be controlled.

A fifth aspect relates to, as the first aspect, the removal of theoscillating. In particular, the fifth aspect relates to an apparatus fordetermining information relating to a projectile, the apparatuscomprising:

-   -   means for receiving electromagnetic radiation emitted from or        reflected by the projectile at least partly while it is in        flight, and for providing a corresponding signal,    -   means for generating an altered signal by removing, from the        provided signal, an oscillating signal, and    -   means for determining the information relating to the projectile        from the altered signal.

The present receiving means may be a single receiving means or bemultiple receiving means positioned in predetermined positions inrelation to each other in order for the receiving means to be able toe.g. determine from where the radiation is received.

The receiving means may be adapted to receive the radiation/sound atmultiple positions and thereby be adapted to provide an altered signalfor each receiving means. This may provide additional information, suchas three-dimensional or two-dimensional information relating to theprojectile.

Again, radiation of any wavelength and e.g. sound may be used for thepresent determination.

In one embodiment, the generating means are adapted to perform anaveraging operation comprising averaging the provided signal over apredetermined time period. In this manner, when the predetermined timeperiod exceeds a period of the oscillating signal, this signal may beaveraged out.

Also, the generating means may be adapted to track the oscillatingsignal and subtract the oscillating signal from the provided signal.This also makes it possible to remove the oscillating signal. In fact,it makes it possible to also derive the oscillating signal and deriveinformation there from—see below.

Preferably, the generating means are adapted to generate the alteredsignal for a predetermined period of time after, that the providedsignal reaches zero. In this manner, when the oscillating signal has alarge amplitude compared to that of the altered signal, thedetermination of the altered signal may be continued even though theoscillating signal extinguishes it for a period of time.

As mentioned above, the receiving means are preferably adapted toreceive the radiation from at least two different directions. Thereceiving means need not be angle sensitive in that the interference isremoved by the present generating means. However, if the oscillatingsignal is caused by multiple paths of the radiation, its detectionrequires detection of the radiation from these paths.

In one embodiment, the determining means are adapted to determine aparameter of the projectile at a first point in time and to estimate,from the determined parameter, the parameter at a second, later, pointin time. In one situation, the determining means are adapted to performthe estimation using a predetermined relation between the parameter andtime. This relation may be provided empirically or may be determined onthe basis of a theory. One parameter to determine is a distance betweenthe receiving means and the projectile.

The receiving means may be adapted to provide the corresponding signalrepresenting an intensity/signal strength/amplitude of the radiationreceived. Then, the determining means may be adapted to determine adistance between the receiving means and the projectile. This isespecially so, if the reflection/emission characteristics of theprojectile are known or even constant, which makes the distancedetermination easier.

In a particularly interesting embodiment, the generating means areadapted to generate the altered signal, until the altered signal fulfilsa predetermined criterion, the determining means being adapted toprovide, as the information, an estimate of a landing point of theprojectile. As mentioned above, this enables the method and apparatus tomake a better estimation of the landing point. Also, the criteria may bedetermined within a wide variety of possibilities depending on thesituation.

Then, the determining means could be adapted to provide, as theinformation, an estimate of a distance between the landing point of theprojectile and a predetermined target. In this manner, it may be desiredto know the positional relation between the receiver and the target.This relation may also comprise a height difference between the receiverand the target.

Alternatively or in addition, the determining means could be adapted toprovide as the information an estimate of a deviation from apredetermined direction and a determined direction of the projectile.Different types of deviations are described above. This provides anothertype of coordinate system in which the projectile path is analyzed. Thistype of analysis may be desired in order to evaluate the differencebetween an aiming direction and the actual direction of the projectile.

Especially in the last situation, the determining means could furthercomprise means for determining a launch position of the projectile, thedetermining means being adapted to provide the determined direction ofthe projectile as a direction between the launch position and thelanding point. Determining the launch position instead of dictating itprovides a better user-friendliness and facilitates use of the apparatusin field operations where fixed positions are not usual.

As mentioned above, one manner of removing the oscillating signal is toperform a suitable averaging. One manner of averaging is to have thegenerating means comprise means for filtering the provided signal usinga time constant larger than a period of the oscillating signal, thedetermining means being adapted to determine a landing point as a pointwhere the signal level has decreased a predetermined amount, such as 3dB.

A sixth aspect relates to an apparatus of determining informationrelating to a projectile, the apparatus comprising:

-   -   means for receiving electromagnetic radiation emitted from or        reflected by the projectile at least partly while it is in        flight, and for providing a corresponding signal,    -   means for identifying whether an amplitude of the provided        signal varies more than a predetermined threshold,    -   means for determining the information from the corresponding        signal, and    -   means for quantifying an uncertainty of the determination of the        information from the variation of the amplitude.

As is the case in the second aspect, this means that the oscillatingsignal need not be removed but that the results (the information) takethis “error” signal into account.

Then, the generating means may be adapted to perform an averagingoperation comprising averaging the provided signal over a time periodlarger than a predetermined time period. This may then be used forquantifying the oscillating signal and the uncertainty.

Naturally, the fifth and sixth aspects may be combined, whereby thesixth aspect may also comprise generating means for generating analtered signal by removing an oscillating signal from the providedsignal, the determining means being adapted to provide additionalinformation relating to the projectile from the altered signal.

Then, the generating means may be adapted to track the oscillatingsignal and subtract the oscillating signal from the provided signal.Also, the generating means could be adapted to generate the alteredsignal for a predetermined period of time after, that the providedsignal reaches zero.

In general, the receiving means are preferably adapted to receive theradiation from at least two different directions.

In one embodiment, the determining means are adapted to determine aparameter of the projectile at a first point in time and estimate, fromthe determined parameter, the parameter at a second, later, point intime. Then, the determining means may be adapted to perform anestimation using a predetermined relation between the parameter andtime. Also, the determining means are preferably adapted to determine aparameter being a distance between a means receiving the radiation andthe projectile.

In a preferred embodiment, the receiving means are adapted to provide acorresponding signal representing an intensity of the radiation receivedand wherein the determining means are adapted to determine a distancebetween the receiving means receiving the radiation and the projectile.

As the third aspect, a seventh aspect relates to the use of theoscillating signal. This embodiment relates to an apparatus ofdetermining information relating to the surroundings of a projectile,the apparatus comprising:

-   -   means for receiving electromagnetic radiation emitted from or        reflected by the projectile at least partly while it is in        flight, and for providing a corresponding signal,    -   means for generating an altered signal by isolating, from the        provided signal, an oscillating signal, and    -   means for determining, as the information and from the altered        signal, an angle to vertical of, and/or a distance to, a surface        over which the projectile flies and/or a reflection coefficient        of the radiation of a surface over which the projectile flies.

Naturally, this may be combined with a means for providing informationrelating to a position of the projectile. This means may be oneaccording to any of the first, second, fifth, and sixth aspects.

In any of the fifth-seventh aspects, as well as the eighth aspectmentioned below, the receiving means are preferably adapted to providethe corresponding signal as a signal representing an intensity or powerof the received radiation within a predetermined frequency/wavelengthinterval and/or the apparatus preferably further comprises means forproviding electromagnetic radiation toward the projectile while inflight,

An eighth aspect of the invention relates to an apparatus of determininga distance between a projectile and a radiation receiver, the apparatuscomprising:

-   -   means for receiving electromagnetic radiation emitted from or        reflected by the projectile at least partly while it is in        flight,    -   means for determining an intensity of the radiation received and        a distance between the receiver and the projectile at a first        point in time,    -   means for determining, at a second, later point in time, a        second intensity of the radiation received, and    -   means for determining from a mathematical relation between the        first and second intensities determined, a distance, at the        second point in time, between the receiver and the projectile.

This aspect relates to the fourth aspect mentioned above.

A ninth aspect relates to a method of determining information relatingto a projectile, the method comprising:

-   -   receiving electromagnetic radiation emitted from or reflected by        the projectile at least partly while it is in flight, and        providing a corresponding signal,    -   determining an expected oscillation of the corresponding signal,        and    -   determining the information from a deviation between the        corresponding signal and the expected oscillation.

When the oscillation relates to the multipath problem stated above, theoscillation may be estimated from e.g. knowledge of the path of theprojectile. This deviation may be calculated from parameters relating tothe projectile, its path and/or surroundings of the projectile. Then,both the signal strength and the amplitude oscillation may be determinedand compared to the provided signal. Deviations there from may be causedby deviations in the path of the projectile compared to that used in theestimation. Such a deviation in the path of the projectile may be thatthe projectile has, in fact, actually landed.

In that manner, the information may be derived from a deviation, such asa deviation between the corresponding signal and the estimatedoscillation.

The estimated oscillation may be an estimate of the amplitude orperiod/frequency of the provided signal as a function of time.

The deviation may be a deviation in intensity/signal strength or in thephase of the estimated signal compared to the estimated oscillation.Other types of deviations or other criteria which the deviation shouldfulfil are described further above.

In addition, a step of identifying whether the amplitude of the providedsignal varies more than a predetermined threshold may be added in orderto determine whether an oscillation large enough is present for it to betaken into account. Also, the presence of this variation may be anindication of that the projectile is close to the ground.

An interesting piece of information to derive is the landing point ofthe projectile. This may be estimated (as the information) from thedeviation in that the provided signal will drop, when the projectile haslanded. Then, the provided signal will deviate from the estimatedoscillation which does not foresee the drop. Then, e.g. a drop of thesignal of a predetermined amount may be used for determining the landingpoint. The actual landing point may be determined on the basis ofknowledge of the trajectory of the projectile while flying.

It should be remembered that the provided signal may, when theoscillation is large, actually become lower than the detection threshold(become zero). However, the estimation of the variation may take thisinto account, whereby this will not interfere with the correctdetermination of the information, such as the landing point.

A tenth aspect relates to an apparatus of determining informationrelating to a projectile, the apparatus comprising:

-   -   means for receiving electromagnetic radiation emitted from or        reflected by the projectile at least partly while it is in        flight, and for providing a corresponding signal,    -   means for determining an expected oscillation of the provided        signal, and    -   means for determining the information from a deviation between        the corresponding signal and the expected oscillation.

The advantages described in relation to the ninth aspect relate equallyto this aspect.

An especially interesting embodiment or group of embodiments is onewhere a plurality of receiving means are used or the radiation isdetermined at a plurality of displaced positions. In this manner, thedifferent detections may be used for deriving additional information.

This additional information may relate to the position of the projectilein that the angle(s) of incident radiation may now be determined, suchas by measuring an amplitude or phase difference between the radiationdetermined at a plurality of positions. Preferably, the positionalrelationship between the positions is known.

In addition, the plurality of determinations of the radiation may also,or optionally, be used for providing further statistics in themeasurement in that a mathematical operation may be performed (e.g. oninformation that may be provided from e.g. a single determination) inorder to increase the certainty of the determination.

The above-mentioned oscillating signal may, in addition to vary theamplitude of the signal received, cause a determination of the angledetected (using the radiation received at a plurality of positions) tobe uncertain. Thus, the removal or tracking of the oscillating signalwill also improve the certainty on an angle determination—and thereby onthe position determination. This is important in a number of situations,such as when wishing to determine the landing point of the projectile.

Preferably, in the method of the first aspect:

-   -   the receiving step comprises receiving radiation at a plurality        of spatially displaced positions and providing a provided signal        for each position,    -   the generating step comprises generating an altered signal for        each provided signal, and    -   the determining step comprises determining the information on        the basis of all provided signals.

Naturally, the filtering, averaging etc. described above may beperformed on each individual signal or after combining the signals.

The altered signals may, for a number of the provided signals, beidentical. However, there may also be differences between the providedsignals in that e.g. phase shifts may be caused by the differentpositions for the detection.

In this context, a spatial displacement simply means that the radiationis received at a plurality of different positions. These positions mayhave differing heights over a ground plane and may have different anglesto the trajectory of the projectile. Naturally, different displacementsgive different advantages depending on the directions or anglespreferably determined.

The determination may then be the determination of a position, angle,velocity, or any other of the above-mentioned types of informationrelevant to a flying or landing projectile. The information may also bea combination of this information, such a trajectory and a landing pointin time so that the landing point position may be determined.

In the second aspect, preferably:

-   -   the receiving step comprises receiving radiation at a plurality        of spatially displaced positions and providing a provided signal        for each position,    -   the identifying step is performed for each provided signal,    -   the determining step comprises determining the information on        the basis of all provided signals, and    -   the quantifying step is performed on the basis of the variation        of the amplitudes of all provided signals.

Naturally, the quantifying step may be a quantification based on eachindividual position, which quantifications are then subsequentlyassembled into a single, overall uncertainty. Alternatively, it may bedetermined initially as the overall uncertainty.

In the third aspect, preferably:

-   -   the receiving step comprises receiving radiation at a plurality        of spatially displaced positions and providing a provided signal        for each position,    -   the generating step is performed for at least two of the        provided signals, and    -   the determining step comprises determining the information on        the basis of all generated, altered signals.

As mentioned above, the oscillating signals need not be different at allpositions, whereby it may not be required to actually determine or track(derive or remove) the oscillating signal individually for eachposition.

In the fourth aspect, preferably:

-   -   the receiving step comprises receiving radiation at a plurality        of spatially displaced positions and providing a provided signal        for each position,    -   the steps of determining intensities comprises determining the        intensities at each position, and    -   the step of determining the distance comprises determining the        distance on the basis of all intensities determined.

In this embodiment, a distance estimate may be derived for eachposition, which estimates are then subsequently merged (such asaveraged). Alternatively, a single distance is determined from theintensities (which may then alternatively be merged prior to thedetermination of the distance).

In the fifth aspect, preferably:

-   -   the receiving step comprises receiving radiation at a plurality        of spatially displaced positions and providing a provided signal        for each position,    -   the step of determining the expected oscillation comprises        determining an expected oscillation for at least one of the        positions, and    -   the step of determining the information comprises determining        the information on the basis of the deviation between at least        one pair of an expected oscillation and the corresponding        provided signal.

As mentioned above, an expected oscillation may be relevant to aplurality of the positions, whereby it is not required to determine anexpected oscillation individually for each position.

From the deviation of the oscillation of one pair of an expectedoscillation and the corresponding provided signal, certain information,such as a landing time, may be derived. However, it is preferred that anexpected oscillation is actually determined for a plurality of thepositions. Then, the deviation will be performed on a number of suchpairs. In that manner, a better estimation of e.g. the angle and therebyposition of the projectile may be obtained, whereby a better estimationof the landing spot position is obtained.

In the sixth aspect, preferably:

-   -   the receiving means comprise a plurality of spatially displaced        receiving means each adapted to provide a provided signal,    -   the generating means area adapted to generate an altered signal        for each receiving means, and    -   the determining means are adapted to determine the information        on the basis of all provided signals.

This is parallel to the above-mentioned preferred embodiment of thefirst aspect.

In the seventh aspect, preferably:

-   -   the receiving means comprise a plurality of spatially displaced        receiving means each adapted to provide a provided signal,    -   the identifying means performed for each provided signal,    -   the determining means are adapted to determine the information        on the basis of all provided signals, and    -   the quantifying means is adapted to perform the quantification        on the basis of the variation of the amplitudes of all provided        signals.

This is parallel to the above-mentioned preferred embodiment of thesecond aspect.

In the eight aspect, preferably:

-   -   the receiving means comprise a plurality of spatially displaced        receiving means each adapted to provide a provided signal,    -   the generating means is adapted to generate an altered signal        for each of at least two of the provided signals, and    -   the determining means is adapted to determine the information on        the basis of all generated, altered signals.

This is parallel to the above-mentioned preferred embodiment of thethird aspect.

In the ninth aspect, preferably:

-   -   the receiving means comprise a plurality of spatially displaced        receiving means each adapted to provide a provided signal,    -   the means for determining intensities are adapted to determine        the intensities at each receiving means, and    -   the means for determining the distance is adapted to determine        the distance on the basis of all intensities determined.

This is parallel to the above-mentioned preferred embodiment of thefourth aspect.

In the tenth aspect, preferably:

-   -   the receiving means comprise a plurality of spatially displaced        receiving means each adapted to provide a provided signal,    -   the means for determining the expected oscillation is adapted to        determine an expected oscillation for at least one of the        receiving means, and    -   the means for determining the information is adapted to        determine the information on the basis of a deviation between at        least one pair of an expected oscillation and the corresponding        provided signal.

This is parallel to the above-mentioned preferred embodiment of thefifth aspect.

It is clear that the above aspects relate to overlapping effects andtechnologies, whereby any two or more thereof may be combined in orderto obtain even better products.

In the following, a preferred embodiment will be described withreference to the drawing, wherein:

FIG. 1 shows the positioning of the radar relative to the trackingobject trajectory as well as a reflective surface,

FIG. 2 shows an example of a ball trajectory with reference to the radarposition,

FIG. 3 shows the received signal intensity of the different receivedsignals,

FIG. 4 is a vector diagram showing the multipath signal adding with thedirect reflected signal,

FIG. 5 shows the process flow to isolate and quantify the multipathsignal,

FIG. 6 shows schematically the position of the transmitter and receiversof the system,

FIG. 7 shows the normalized received signal intensity in both presenceand absence of multipath signals,

FIG. 8 shows the output of the sliding RMS detector in both presence andabsence of multipath signals,

FIG. 9 shows an electronic functional block diagram of the system,

FIG. 10 shows the received signal intensity of two different receivers,and

FIG. 11 shows elevation angle measurement derived from the monopulsephase.

In the preferred embodiment of the present invention, the transmitter 27is a continuous wave (CW) signal being emitted from an antenna 15co-located with at least one receiving antenna, i.e. a CW Doppler radar.In the preferred embodiment, the receiver consists of at least threeseparate receiving antennas 16-18, enabling use of the well knownmonopulse measuring principle to measure the angle to the projectile,see “Introduction to Radar Systems” Third Edition, Merril I. Skolnik,which is incorporated herein as reference. An electrical functionalblock diagram of the system is shown in FIG. 9.

In the preferred embodiment, the projectile is a sports ball, a specialinterest is related to the case of a golf ball, where there is highcommercial interest of being able to measure the exact trajectory,including precise determination of the landing point. In the followingdescription the measuring object in flight will be referred to as aball, but can be any type of a solid object traveling through the air,such as projectiles, missiles, airplanes and other sports balls.

The antennas can be arranged as shown in FIG. 6, but many othercombinations are possible. The receiving antennas 16 and 17 arevertically spaced a distance DV, where as the receiving antennas 17 and18 are horizontally spaced a distance DH. In this way the phasedifference ΔV between the signal from a ball recorded by receivingantennas 16 and 17 will be directly related to the vertical angle E fromthe radar to the ball through [eq. 1]. The phase difference ΔH betweenreceiving antennas 17 and 18 will consequently be directly related tothe horizontal angle A from the radar to the ball through [eq. 2].ΔV=2n*DV/λ*sin(E)   [eq. 1]

-   -   , where λ is the radar wavelength        ΔH=2n*DV/λ*sin(A)   [eq. 2]

In the preferred embodiment of the present invention, the phasedifferences between receiving antennas 16-18 are measured by using thephase-phase monopulse principle on the recorded signals. However, manyother standard techniques can be used for this, like theamplitude-amplitude monopulse principle, as outlined in the publication“Introduction to Radar Systems” Third Edition, Merril I. Skolnik, whichis incorporated herein as reference again.

The radar return signal from a CW Doppler radar consists of a number ofcontinuous signals x(t) corresponding each to the relative position andmovement of the reflective objects in front of the radar. In thefollowing the situation only one reflective object, the ball, isconsidered, but the description holds as well for multiple reflectiveobjects. In this case the received signal z_(rx)(t) of one of thereceivers 16-18 only consist of the direct reflected signal x(t) fromthe ball, see [eq. 3].z _(rx)(t)=x(t)   [eq. 3]

The amplitude of the x(t), a(t) is determined by the radar cross sectionof the ball as well as the distance from the radar and radar gain in thespecific direction of the ball, see [eq. 4].|x(t)|² =a(t)² =Ptx*Gtx*Grx*RCS*λ ²/((4*n)³ *R ⁴)   [eq. 4]

-   -   , where:    -   Ptx is the transmitted power    -   Gtx is the transmitting antenna gain in direction of ball    -   Grx is the receiving antenna gain in direction of ball    -   RCS is the radar cross section of ball    -   λ is the the radar wavelength    -   R is the distance from radar to ball

In most practical situations not only the direct reflected signal, R, 5is received from the ball 1, flying along a trajectory 40 between alaunch position 38 and a landing point 39, also a multipath reflectedsignal, Rmp, 6 is received, see FIG. 1. The resulting received signalz_(rx)(t) can be described by [eq. 5].z _(rx)(t)=x(t)+x _(mp)(t)=x(t)*(1+e _(mp)(t))   [eq. 5]

-   -   , where:    -   x(t) is the received signal of the direct reflected ray 5 from        the ball 1    -   x_(mp)(t)=x(t)*e_(mp)(t) received signal of the multipath        reflected ray 6 from the ball 1.    -   e_(mp)(t) is the modulation of the multipath reflected signal 6        relative to the direct reflected signal 5.

In the following only one multipath signal will be considered, but thegeneral principles are also applicable on multiple multipath signals.

The multipath reflected signal 6 will be highly correlated with thedirect reflected signal 5, but will include a modulation, described bye_(mp)(t). e_(mp)(t) will depend on the geometry and reflectioncharacteristics of the ball and the reflecting point 4. e_(mp)(t), wherethe reflecting point is on a reflecting surface (illustrated by ahorizontal line) can be described by [eq. 6].

e _(mp)(t)=√(δRCS*ρ _(g) *dG)*(R/Rmp)²*exp(−j*2n*dR/λ)=a_(mp)(t)*exp((φ_(mp)(t))   [eq. 6]

-   -   , where:    -   δRCS is the reflection difference in multipath geometry compared        to direct reflection    -   ρ_(g) is the reflection coefficient of the ground    -   dG is the radar gain difference for the incoming multipath        reflected ray    -   dR is the path length difference between multipath ray 6 and        direct reflected ray 5.    -   λ is the wavelength of the radio wave

For an object propagating in a stationary environment, i.e. multipathreflection point 4 does not jump around, the modulation signal e_(mp)(t)will be a slowly varying oscillating signal dictated by the variation ofthe path length difference dR.

The path length difference dR can be mathematically expressed from thegeometry in FIG. 1 by [eq. 7].dR=Rmp−R=R(√(1+4*y*hr/R ²)−1)   [eq. 7]

-   -   , where:    -   hr is the height of the receiving antenna above the reflecting        surface    -   y is the height of the ball above the reflecting surface

Assuming a ball trajectory (see FIG. 2), observed by a radar 2, thereceived power over time will be as shown in FIG. 3. In FIG. 3, 7 is thereceived power |x(t)|² from the direct reflected ray 5 alone, graph 8 isthe received power |x_(mp)(t)|² from the multipath reflected ray 6alone. The resulting received power |z_(rx)(t)|² (graph 9) shows anoscillating signal around the power received from the direct reflectedray, graph 7. It is realized that the oscillation of 9 is directlyrelated to the variation of e_(mp)(t) coherently adding with a unityvector representing the normalized direct reflected signal x(t), as canbe seen in the vector diagram in FIG. 4.

The period, Tmp, of the oscillation of 9 is given by when dR changes λ.Tmp is typically in the interval of 0.1-2 seconds for sports balltrajectories with radar 2 placed close to some part of the trajectory.

If more receivers are present like in FIG. 9, the heights hr of theindividual receiving antennas are in general not the same. This meansthat dR is slightly different at a given point in time for the differentreceivers, this introduces a phase difference of the oscillating signalpower between the different receivers in the multipath scenario. In FIG.10 the received power |z_(rx)(t)|² for receiving antenna 17 is plottedas 9 together with the received power |z_(rx)(t)|² for receiving antenna16 which also plotted as 35. In FIG. 10 the received power |x(t)|² fromthe direct reflected ray 5 alone is shown as 7 for comparison.

Due to the phase difference of the oscillating signals of the differentreceivers, the monopulse phase difference will be distorted in amultipath scenario. In FIG. 11 the vertical angle 36 derived from [eq.1] is shown for the case of only the direct reflected ray 5, and alsothe vertical angle 37 in the case of presence of multipath signals isshown.

Determination of Presence of Multipath Signals

The process of detecting the presence of multipath signals in thereceived signal z_(rx)(t) is shown in FIG. 5.

First the tracking is established 10 as normally done with Dopplerradars, i.e. tracking the Doppler frequency generated by the moving ballover time. From the recorded data of the at least three receivers, thethree dimensional position is calculated 11 without knowing whether amultipath signal is present or not. The range R to the ball iscalculated as an integration of the tracked Doppler frequency fromlaunch time and adding the assumed distance between the radar and thelaunch position 38. The vertical and horizontal angles are calculatedfrom [eq. 1] and [eq. 2]. If a multipath signal is present this willintroduce an error in the three dimensional position through distortionon the vertical (and horizontal) angle as illustrated in FIG. 11. Heavyfiltering (averaging) is done on the angles to reduce the negativeinfluence on the three dimensional position, the time constant on theangle filtering should be higher than the period of the oscillation Tmp.

All the three received signals are then normalized 12 for the known timevariation of the direct reflected signal power as can be derived from[eq. 4].

The normalization equation is:z _(n,rx)(t)=z _(rx)(t)*R ²/√(Gtx*Grx*RCS)   [eq. 8]

-   -   , where:    -   Gtx is the transmitting antenna gain in direction of ball 1    -   Grx is the receiving antenna gain in direction of ball 1    -   RCS is the radar cross section of ball 1

In the case of a spherical symmetrical ball, like golf balls, tennisballs, baseballs, cricket balls and similar, the radar cross section RCSof the ball is to a very high degree constant independent of orientationof the ball relative to the radar. In this case RCS in [eq. 8] can beomitted.

In FIG. 7 the normalized signal power |z_(n,rx)(t)|² is shown. The trace19 corresponds to the normalized signal power without multipath 7, andthe trace 20 corresponds to the normalized signal power with multipath9. The oscillation of 20 is clearly an indication of multipath.

It is noted that the detection of oscillation of power of the normalizedsignal z_(n,rx)(t) can be done in number of different ways. In thefollowing only one of the preferred methods are outlined, but many otherstandard methods may be applied.

To isolate the multipath signal 13 a sliding root-mean-square (RMS)detector on the normalized signal z_(n,rx)(t) is used. The RMS detectoris performed over a time corresponding to the expected period of theoscillation Tmp, and is calculated according to [eq. 9].RMS _(Tmp)(t)=(E{|z _(n,rx)(t)|²}_(t±Tmp/2) −E{|z _(n,rx)(t)|}²_(t±Tmp/2))/(√2*E{|z _(n,rx)(t)|}_(t±Tmp/2))   [eq. 9]

In FIG. 8 the sliding RMS detector RMS_(Tmp)(t) is shown. The trace 25corresponds to the normalized signal power without multipath 7, and thetrace 26 corresponds to the normalized signal power with multipath 9.

To quantify the magnitude of the multipath signal, the output of thesliding RMS detector can be used directly. In fact the value ofRMS_(Tmp)(t) is directly an estimation of a_(mp)(t) in [eq. 6]. Toquantify whether multipath signals is present or not, the output of theRMS detector is compared with a predetermined threshold 14.

The sliding RMS detector as outlined above must in general be appliedseparately on all the three received signals, since the amplitude of theoscillation need not be the same for all the receiving signals.

Once the magnitude of the multipath signal a_(mp)(t) is known, thetracking and smoothing filters can be adjusted to tolerate the errorscaused by the multipath signals. The worst case error in the phasedifferences in [eq. 1] and [eq. 2] are given by:ΔV _(err,W.C.)≈2*A tan(a _(mp)(t))ΔH _(err,W.C.)≈2*A tan(a _(mp)(t))

Using these error margins in the tracking and smoothing filters willenable the ball to be tracked more robust and provide more accurateflight path data.

To detect when the ball has actually landed 39, the knowledge of themultipath level is used.

When the ball is about to land, the signal level of the direct reflectedray 5 is normally at a minimum, due to maximum distance between ball 1and radar 2. Further more, the power of the received multipath signal 6will be only slightly smaller than the direct reflected signal 5, sincethe ground reflection coefficient ρ_(g) is close to 1.0 for parallelincident rays. Consequently the total received signal z_(rx)(t) canreach a minimum that might be under the detection limit, even though theball has not landed. The minimum signal level in the landing scenariohappens exactly when the phase of the multipath signal is 180 degreesout of phase with the direct reflected signal, i.e. when φ_(mp)(t)=−n.This happens exactly the time Tmp/2 before the ball actually lands.Consequently the tracking is always continued at least Tmp/2 after thesignal level has dropped below the detection limit when multipath isdetected as explained above. If the signal reappears after this dropout,it will only reappear for Tmp/2 seconds. These reappearing data aremerged with the previous track.

The landing point is determined as being the last measurement pointincluding any merging of reappearing signals. If the detection of themeasurement point is done by frequency analysis, which extend over somedata points, the time for landing is being determined as being when thesignal level has dropped 3 dB relative to the expected power variationtaking into account the multipath influence. By adding the threereceived signals before detecting the measurement points an increase insignal-to-noise ratio is gained, which will give a more accuratedetermination of the landing time. The final three dimensional landingpoint is calculated by evaluating the smoothed trajectory data at thelanding time determined above. The relative phase of the multipathsignal φ_(mp)(t) can be estimated in a number of different ways. Onemethod is to detect the zero-crossings 21 and 22 (in dB) and minimum 23and maximum 24 of the normalized signal power |z_(n,rx)(t)|² like 20 inFIG. 7. The minimum represent φ_(mp)(t) equal to ±n, the maximumφ_(mp)(t) equal to 0 and finally the zero crossings close to ±n/2. Thisgives two solutions for the slope of the phase φ_(mp)(t), an upwards anda downwards slope. The slope is determined from the sign of thederivative of dR with respect to time, which is calculated from themeasured trajectory during step 11. The final estimation of φ_(mp)(t) isdone by fitting a smooth curve to the found phase points above.

The estimation of the phase of the multipath signal must be carried outseparately for each of the receiving signals

Removal of Multipath Signal

Once the presence of the multipath signal has been detected and therelative multipath signal e_(mp)(t) has been estimated, it is possibleto remove the multipath signal from the received signals by altering thereceiver signal according to [eq. 10].x _(est)(t)=z _(rx)(t)/(1+ê _(mp)(t))   [eq. 10]

Then the three dimensional position can be re-calculated from thealtered receiver signals x_(est)(t). The trajectory data derived fromthe altered receiver signals will to a high degree be cleaned formultipath distortion on the vertical and horizontal angles. Further thealtered signal will not experience the oscillation, and possibledropouts just before landing, thus given a much better accuracy on theestimation of landing time and thereby more accurate landing position.

Range and RCS Measurement from Signal Power Level

In the following all the receiver signals are either cleaned foroscillating signals as explained above [eq. 10], or averaged out theoscillation in the normalized z_(n,rx)(t) similar to [eq. 8] and theninverse normalization of [eq. 6] to get z_(rx)(t), or the level of themultipath signal is below a certain limit not to affect the receivedpower level according to [eq. 3].

In relation to range measurement of Doppler radar signals, all previousinventions have analyzed the radar return from a single fixed frequencyDoppler radar only for the frequency shift generated by the apparentvelocity Vr of the ball moving in front of the radar, or more preciselythe change in range over time (sometimes denoted range rate),mathematically dR/dt.

To calculate the distance R to the ball, all previous Doppler radarinventions have integrated the range rate Vr from a known referencepoint. Consequently the distance R is a derived measurement from thedirectly measured range rate Vr and it requires a fix point.

The present invention presents a novel method to actually measure thedistance R to the ball by proper analyzing of the radar return signalfrom a Doppler radar. The distance R is measured independently from themeasured range rate.

The direct measured distance R in a Doppler radar system can be used inmany different applications and scenarios. More generally speaking thedirect measured range adds a new independent measured parameter for aDoppler radar.

The present invention measures the distance R to the ball by measuringthe signal level Prx corresponding to the tracking object. The preferredmethod to measure the signal level of a given tracking object is byfrequency analyzing methods, but other methods may also be applied.

The distance R to the ball is calculated from the received signal levelPrx by using the radar equation inversely:R=((Ptx/Prx*Gtx*Grx*λ ²)/(4n)³ *RCS)^(0.25)   [eq. 11]

All the parameters on the right hand side above, are system parametersthat are known except for the radar cross section RCS of the ball.

The antenna gain of the Doppler radar in the transmitter Gtx andreceiver Grx can vary inside the coverage volume of the radar. However,if the sighting angle to the target is known, this inaccuracy can beremoved by using the known radiation pattern of the transmitting andreceiving antennas.

In a monopulse Doppler radar system, the sighting angle to the targetcan be measured independently of the range rate Vr and the distance R.This means that in such a system the only unknown on the right hand sideof [eq. 11] is the RCS.

Equation [eq. 11] can be simplified to [eq. 12], where M is the measuredsignal level adjusted for system parameters.R=M*RCS ^(0.25), M=((Ptx/Prx*Gtx*Grx*L*λ ²)/(4n)³)^(0.25)   [eq. 12]

In some cases the RCS of the ball is known a priori. In this case [eq.12] can be used directly to measure the distance R.

In other cases only the relative level of RCS is known when viewing theball from different aspect angles, i.e. RCS=RCSo*func((φ,θ) where RCSois unknown. In this case [eq. 12] can be rewritten to [eq. 13], where M′includes the known func((φ,θ)^(0.25) variation of the RCS.R=M′*RCSo ^(0.25), M′=M*func((φ,θ)^(0.25)   [eq. 13]

In this case the ball is observed at minimum two different distances,see [eq. 14-15] where the relative change in distance is measured byintegration of the measured range rate Vr.R(n)=M′(n)*RCSo ^(0.25)   [eq. 14]R(n+1)=R(n)+ΔR=M′(n+1)*RCSo ^(0.25), ΔR=int(n,n+1,Vr)   [eq. 15]

RCSo can now be calculated from [eq. 16]:RCSo=(ΔR/(M′(n+1)−M′(n)))⁴   [eq. 16]

After having found RCSo, [eq. 13] is used directly to measure thedistance R.

Spherically shaped targets are a special interesting group of targets.This type of targets includes also targets that are nearly spherical.Examples include small projectiles, calibration spheres and mostsporting balls (golf ball, base ball, foot/soccer ball, tennis ball,cricket ball etc.). The spherically shaped targets has the advantagethat the RCS is constant independent of orientation of target(func((φ,θ)=1), and that it is relatively simple to theoreticallypredict the RCS from given dimensions and material characteristics.

Reflection Coefficient and Position of Reflection Point

When the relative phase φ_(mp)(t) of the multipath signal has beenestimated as outlined above, the variation of dR over time is also knownthrough [eq. 6]. When dR is known, [eq. 7] can be used to estimate theheight hr of the radar 2 above the reflection point, where R and y aretaken from the measured three dimensional position of the ball. The onlyassumption is that the reflecting surface is horizontal.

When the height hr is known, also the angle Emp in FIG. 1 can be found,this means that the reflection point can be positioned threedimensionally.

By also having the estimation of the relative amplitude a_(mp)(t) of themultipath signal, the reflection coefficient ρ_(g) of the reflectingsurface can be estimated using [eq. 6] inversely.

1-68. (canceled)
 69. A method of determining information relating to aprojectile, the method comprising: receiving electromagnetic radiationemitted from or reflected by the projectile at least partly while it isin flight, and providing a corresponding signal, generating an alteredsignal by removing, from the provided signal, an oscillating signal, anddetermining the information relating to the projectile from the alteredsignal.
 70. A method according to claim 69, wherein the generating stepcomprises performing an averaging operation comprising averaging theprovided signal over a predetermined time period.
 71. A method accordingto claim 69, wherein the generating step comprises tracking theoscillating signal and subtracting the oscillating signal from theprovided signal.
 72. A method according to claim 69, wherein thegenerating step comprises generating the altered signal for apredetermined period of time after, that the provided signal reacheszero.
 73. A method according to claim 69, wherein the receiving stepcomprises receiving the radiation from at least two differentdirections.
 74. A method according to claim 69, wherein the determiningstep comprises determining a parameter of the projectile at a firstpoint in time and estimating, from the determined parameter, theparameter at a second, later, point in time.
 75. A method according toclaim 74, wherein the estimation is performed using a predeterminedrelation between the parameter and time.
 76. A method according to claim74, wherein the parameter determined is a distance between a meansreceiving the radiation and the projectile.
 77. A method according toclaim 69, wherein the corresponding signal provided is a signalrepresenting an intensity of the radiation received and wherein thedetermining step comprises determining a distance between a meansreceiving the radiation and the projectile.
 78. A method according toclaim 69, wherein the generating step comprises generating the alteredsignal, until the altered signal fulfils a predetermined criterion, thedetermining step comprising providing, as the information, an estimateof a landing point of the projectile.
 79. A method according to claim78, wherein the determining step comprises providing as the informationan estimate of a distance between the landing point of the projectileand a predetermined target.
 80. A method according to claim 78, whereinthe determining step comprises providing as the information an estimateof a deviation from a predetermined direction and a determined directionof the projectile.
 81. A method according to claim 80, wherein thedetermining step further comprises determining a launch position of theprojectile, the determined direction of the projectile being a directionbetween the launch position and the landing point.
 82. A methodaccording to claim 78, wherein the generating step comprises performinga filtering using a time constant larger than a period of theoscillating signal and wherein the determining step comprisesdetermining the landing point as a point where the signal level hasdecreased a predetermined amount.
 83. A method of determininginformation relating to a projectile, the method comprising: receivingelectromagnetic radiation emitted from or reflected by the projectile atleast partly while it is in flight, and providing a correspondingsignal, identifying whether an amplitude of the provided signal variesmore than a predetermined threshold, determining the information fromthe corresponding signal, and quantifying an uncertainty of thedetermination of the information from the variation of the amplitude.84. A method according to claim 83, wherein the generating stepcomprises performing an averaging operation comprising averaging theprovided signal over a time period larger than a predetermined timeperiod.
 85. A method according to claim 83, further comprising a step ofgenerating an altered signal by removing an oscillating signal from theprovided signal, the method further comprising the step of determiningfurther information from the altered signal.
 86. A method according toclaim 85, wherein the generating step comprises tracking the oscillatingsignal and subtracting the oscillating signal from the provided signal.87. A method according to claim 85, wherein the generating stepcomprises generating the altered signal for a predetermined period oftime after, that the provided signal reaches zero.
 88. A methodaccording to claim 83, wherein the receiving step comprises receivingthe radiation from at least two different directions.
 89. A methodaccording to claim 83, wherein the determining step comprisesdetermining a parameter of the projectile at a first point in time andestimating, from the determined parameter, the parameter at a second,later, point in time.
 90. A method according to claim 89, wherein theestimation is performed using a predetermined relation between theparameter and time.
 91. A method according to claim 89, wherein theparameter determined is a distance between a means receiving theradiation and the projectile.
 92. A method according to claim 83,wherein the corresponding signal provided is a signal representing anintensity of the radiation received and wherein the determining stepcomprises determining a distance between a means receiving the radiationand the projectile.
 93. A method of determining information relating tothe surroundings of a projectile, the method comprising: receivingelectromagnetic radiation emitted from or reflected by the projectile atleast partly while it is in flight, and providing a correspondingsignal, generating an altered signal by isolating, from the providedsignal, an oscillating signal, and determining, as the information andfrom the altered signal, an angle to vertical of, and/or a distance to,a surface over which the projectile flies and/or a reflectioncoefficient of the radiation of a surface over which the projectileflies.
 94. A method according to claim 69, wherein the step of providingthe corresponding signal comprises providing a signal representing anintensity or power of the received radiation within a predeterminedfrequency/wavelength interval.
 95. A method according to claim 69, themethod further comprising the initial step of providing electromagneticradiation toward the projectile while in flight.
 96. A method ofdetermining a distance between a projectile and a radiation receiver,the method comprising the steps of: receiving electromagnetic radiationemitted from or reflected by the projectile at least partly while it isin flight, determining an intensity of the radiation received and adistance between the receiver and the projectile at a first point intime, determining, at a second, later point in time, a second intensityof the radiation received, and determining from a mathematical relationbetween the first and second intensities determined, a distance, at thesecond point in time, between the receiver and the projectile.
 97. Anapparatus for determining information relating to a projectile, theapparatus comprising: means for receiving electromagnetic radiationemitted from or reflected by the projectile at least partly while it isin flight, and for providing a corresponding signal, means forgenerating an altered signal by removing, from the provided signal, anoscillating signal, and means for determining the information relatingto the projectile from the altered signal.
 98. An apparatus according toclaim 97, wherein the generating means are adapted to perform anaveraging operation comprising averaging the provided signal over apredetermined time period.
 99. An apparatus according to claim 97,wherein the generating means are adapted to track the oscillating signaland subtract the oscillating signal from the provided signal.
 100. Anapparatus according to claim 97, wherein the generating means areadapted to generate the altered signal for a predetermined period oftime after, that the provided signal reaches zero.
 101. An apparatusaccording to claim 97, wherein the receiving means are adapted toreceive the radiation from at least two different directions.
 102. Anapparatus according to claim 97, wherein the determining means areadapted to determine a parameter of the projectile at a first point intime and estimate, from the determined parameter, the parameter at asecond, later, point in time.
 103. An apparatus according to claim 102,wherein the determining means are adapted to perform the estimationusing a predetermined relation between the parameter and time.
 104. Anapparatus according to claim 102, wherein the determining means areadapted to determine a parameter being a distance between the receivingmeans and the projectile.
 105. An apparatus according to claim 97,wherein the receiving means are adapted to provide the correspondingsignal representing an intensity of the radiation received and whereinthe determining means are adapted to determine a distance between thereceiving means and the projectile.
 106. An apparatus according to claim97, wherein the generating means are adapted to generate the alteredsignal, until the altered signal fulfils a predetermined criterion, thedetermining means being adapted to provide, as the information, anestimate of a landing point of the projectile.
 107. An apparatusaccording to claim 106, wherein the determining means are adapted toprovide as the information an estimate of a distance between the landingpoint of the projectile and a predetermined target.
 108. An apparatusaccording to claim 106, wherein the determining means are adapted toprovide as the information an estimate of a deviation from apredetermined direction and a determined direction of the projectile.109. An apparatus according to claim 108, wherein the determining meansfurther comprise means for determining a launch position of theprojectile, the determining means being adapted to provide thedetermined direction of the projectile as a direction between the launchposition and the landing point.
 110. An apparatus according to claim105, wherein the generating means comprise means for filtering theprovided signal using a time constant larger than a period of theoscillating signal, the determining means being adapted to determine alanding point as a point where the signal level has decreased apredetermined amount.
 111. An apparatus of determining informationrelating to a projectile, the apparatus comprising: means for receivingelectromagnetic radiation emitted from or reflected by the projectile atleast partly while it is in flight, and for providing a correspondingsignal, means for identifying whether an amplitude of the providedsignal varies more than a predetermined threshold, means for determiningthe information from the corresponding signal, and means for quantifyingan uncertainty of the determination of the information from thevariation of the amplitude.
 112. An apparatus according to claim 111,wherein the generating means are adapted to perform an averagingoperation comprising averaging the provided signal over a time periodlarger than a predetermined time period.
 113. An apparatus according toclaim 111, further comprising means for generating an altered signal byremoving an oscillating signal from the provided signal, the determiningmeans being adapted to provide additional information relating to theprojectile from the altered signal.
 114. An apparatus according to claim111, wherein the generating means are adapted to track the oscillatingsignal and subtract the oscillating signal from the provided signal.115. An apparatus according to claim 113, wherein the generating meansare adapted to generate the altered signal for a predetermined period oftime after, that the provided signal reaches zero.
 116. An apparatusaccording to claim 111, wherein the receiving means are adapted toreceive the radiation from at least two different directions.
 117. Anapparatus according to claim 111, wherein the determining means areadapted to determine a parameter of the projectile at a first point intime and estimate, from the determined parameter, the parameter at asecond, later, point in time.
 118. An apparatus according to claim 117,wherein the determining means are adapted to perform an estimation usinga predetermined relation between the parameter and time.
 119. Anapparatus according to claim 117, wherein the determining means areadapted to determine a parameter being a distance between a meansreceiving the radiation and the projectile.
 120. An apparatus accordingto claim 111, wherein the receiving means are adapted to provide acorresponding signal representing an intensity of the radiation receivedand wherein the determining means are adapted to determine a distancebetween the receiving means receiving the radiation and the projectile.121. An apparatus of determining information relating to thesurroundings of a projectile, the apparatus comprising: means forreceiving electromagnetic radiation emitted from or reflected by theprojectile at least partly while it is in flight, and for providing acorresponding signal, means for generating an altered signal byisolating, from the provided signal, an oscillating signal, and meansfor determining, as the information and from the altered signal, anangle to vertical of, and/or a distance to, a surface over which theprojectile flies and/or a reflection coefficient of the radiation of asurface over which the projectile flies.
 122. An apparatus according toclaim 97, wherein the receiving means are adapted to provide thecorresponding signal as a signal representing an intensity or power ofthe received radiation within a predetermined frequency/wavelengthinterval.
 123. An apparatus according to claim 97, the apparatus furthercomprising means for providing electromagnetic radiation toward theprojectile while in flight.
 124. An apparatus of determining a distancebetween a projectile and a radiation receiver, the apparatus comprising:means for receiving electromagnetic radiation emitted from or reflectedby the projectile at least partly while it is in flight, means fordetermining an intensity of the radiation received and a distancebetween the receiver and the projectile at a first point in time, meansfor determining, at a second, later point in time, a second intensity ofthe radiation received, and means for determining from a mathematicalrelation between the first and second intensities determined, adistance, at the second point in time, between the receiver and theprojectile.
 125. A method of determining information relating to aprojectile, the method comprising: receiving electromagnetic radiationemitted from or reflected by the projectile at least partly while it isin flight, and providing a corresponding signal, determining an expectedoscillation of the provided signal, and determining the information froma deviation between the corresponding signal and the expectedoscillation.
 126. An apparatus of determining information relating to aprojectile, the apparatus comprising: means for receivingelectromagnetic radiation emitted from or reflected by the projectile atleast partly while it is in flight, and for providing a correspondingsignal, means for determining an expected oscillation of the providedsignal, and means for determining the information from a deviationbetween the corresponding signal and the expected oscillation.
 127. Amethod according to claim 69, wherein: the receiving step comprisesreceiving radiation at a plurality of spatially displaced positions andproviding a provided signal for each position, the generating stepcomprises generating an altered signal for each provided signal, and thedetermining step comprises determining the information on the basis ofall provided signals.
 128. A method according to claim 83, wherein: thereceiving step comprises receiving radiation at a plurality of spatiallydisplaced positions and providing a provided signal for each position,the identifying step is performed for each provided signal, thedetermining step comprises determining the information on the basis ofall provided signals, and the quantifying step is performed on the basisof the variation of the amplitudes of all provided signals.
 129. Amethod according to claim 91, wherein: the receiving step comprisesreceiving radiation at a plurality of spatially displaced positions andproviding a provided signal for each position, the generating step isperformed for at least two of the provided signals, and the determiningstep comprises determining the information on the basis of allgenerated, altered signals.
 130. A method according to claim 96,wherein: the receiving step comprises receiving radiation at a pluralityof spatially displaced positions and providing a provided signal foreach position, the steps of determining intensities comprisesdetermining the intensities at each position, and the step ofdetermining the distance comprises determining the distance on the basisof all intensities determined.
 131. A method according to claim 125,wherein: the receiving step comprises receiving radiation at a pluralityof spatially displaced positions and providing a provided signal foreach position, the step of determining the expected oscillationcomprises determining an expected oscillation for at least one of thepositions, and the step of determining the information comprisesdetermining the information on the basis of the deviation between atleast one pair of an expected oscillation and the corresponding providedsignal.
 132. An apparatus according to claim 97, wherein: the receivingmeans comprise a plurality of spatially displaced receiving means eachadapted to provide a provided signal, the generating means area adaptedto generate an altered signal for each receiving means, and thedetermining means are adapted to determine the information on the basisof all provided signals.
 133. An apparatus according to claim 111,wherein: the receiving means comprise a plurality of spatially displacedreceiving means each adapted to provide a provided signal, theidentifying means performed for each provided signal, the determiningmeans are adapted to determine the information on the basis of allprovided signals, and the quantifying means is adapted to perform thequantification on the basis of the variation of the amplitudes of allprovided signals.
 134. An apparatus according to claim 119, wherein: thereceiving means comprise a plurality of spatially displaced receivingmeans each adapted to provide a provided signal, the generating means isadapted to generate an altered signal for each of at least two of theprovided signals, and the determining means is adapted to determine theinformation on the basis of all generated, altered signals.
 135. Anapparatus according to claim 124, wherein: the receiving means comprisea plurality of spatially displaced receiving means each adapted toprovide a provided signal, the means for determining intensities areadapted to determine the intensities at each receiving means, and themeans for determining the distance is adapted to determine the distanceon the basis of all intensities determined.
 136. An apparatus accordingto claim 126, wherein: the receiving means comprise a plurality ofspatially displaced receiving means each adapted to provide a providedsignal, the means for determining the expected oscillation is adapted todetermine an expected oscillation for at least one of the receivingmeans, and the means for determining the information is adapted todetermine the information on the basis of a deviation between at leastone pair of an expected oscillation and the corresponding providedsignal.
 137. A method according to claim 83, wherein the step ofproviding the corresponding signal comprises providing a signalrepresenting an intensity or power of the received radiation within apredetermined frequency/wavelength interval.
 138. A method according toclaim 93, wherein the step of providing the corresponding signalcomprises providing a signal representing an intensity or power of thereceived radiation within a predetermined frequency/wavelength interval.139. A method according to claim 83, the method further comprising theinitial step of providing electromagnetic radiation toward theprojectile while in flight.
 140. A method according to claim 93, themethod further comprising the initial step of providing electromagneticradiation toward the projectile while in flight.
 141. An apparatusaccording to claim 106, wherein the generating means comprise means forfiltering the provided signal using a time constant larger than a periodof the oscillating signal, the determining means being adapted todetermine a landing point as a point where the signal level hasdecreased a predetermined amount.
 142. An apparatus according to claim111, wherein the receiving means are adapted to provide thecorresponding signal as a signal representing an intensity or power ofthe received radiation within a predetermined frequency/wavelengthinterval.
 143. An apparatus according to claim 121, wherein thereceiving means are adapted to provide the corresponding signal as asignal representing an intensity or power of the received radiationwithin a predetermined frequency/wavelength interval.
 144. An apparatusaccording to claim 111, the apparatus further comprising means forproviding electromagnetic radiation toward the projectile while inflight.
 145. An apparatus according to claim 121, the apparatus furthercomprising means for providing electromagnetic radiation toward theprojectile while in flight.